The problem with “liberal Mormon” is not the liberal Mormons, whoever they might be, but rather the term used to classify them. It seems to me that the term is used as a catch-all for at least five mostly unrelated things.
“Liberal Mormons” sometimes refers to Mormons who are liberals in the vulgar sense of the warped American political spectrum, people who tend to vote for Democrats or have warm feelings towards the welfare state.
As far as I can tell, however, “liberal Mormon” doesn’t usually refer to Mormons who are working-class labor organizers. “Liberal Mormon” has many of the connotations of “Lexus liberal” or “liberal academic”: white, privileged, educated. Sometimes “liberal Mormon” is interchangeable with “Mormon intellectual,” someone who has a better than average acquaintance with issues in church history and theology.
Often, “liberal Mormon” is a matter of scriptural interpretation. “Liberal” in this sense sometimes seems to apply to anyone with less than an ultra-literalist understanding of scriptural historicity. As with “originalists” and “constructionists” in constitutional law, “liberal Mormons” are supposed to line up for an anything-goes, whatever-gets-you-through-the-night reading of inspired fiction, while the alternative is unyielding insistence on a 6,000-year old Earth (not including the recycled planets with dinosaur fossils in them). Like the terms “originalist” and “constructionist,” “liberal Mormon” in the scriptural sense probably obscures more than it enlightens.
A fourth sense of “liberal Mormon” is roughly equivalent to “progressive,” someone with a sense that the church or its leaders or teachings are in some way imperfect or unjust, and that these deficiencies should be identified so that they can be corrected.
Finally, “liberal Mormon” is sometimes the equivalent of “libertine Mormon,” someone for whom some or all of the church’s standards or commandments are optional.
Apart from lumping together people who might strenuously object to the association (qui bono?), “liberal Mormon” seems fated not to label an opponent of “conservative Mormonism” (which barely exists as a category), but rather to identify the opposite of “orthodox Mormon.” That would not be a good thing for anybody, no matter how they read Genesis, Job, and Jonah.